Symmetrizable Boolean networks

被引：3

作者：

Aledo, Juan A. ^{[1
]}

Goles, Eric ^{[2
]}

Montalva-Medel, Marco ^{[2
]}

Montealegre, Pedro ^{[2
]}

Valverde, Jose C. ^{[1
]}

机构：

[1] Univ Castilla La Mancha, Dept Matemat, Albacete 02071, Spain

[2] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Avda Diagonal Torres 2700 Penalolen, Santiago, Chile

来源：

INFORMATION SCIENCES | 2023年 / 626卷

关键词：

Generalized parallel dynamical system; Period structure; Limit cycles; Symmetric and anti-symmetric networks; Symmetrizable networks; DISCRETE DYNAMICAL-SYSTEMS; CELLULAR-AUTOMATA; COMPUTATIONAL-COMPLEXITY;

D O I：

10.1016/j.ins.2023.01.082

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i. e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.

引用

页码：787 / 804

页数：18

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